Am I reading this right? Between rounds, like on any level in Day 2, you should do a 3 min. rest? I've been jumping from one round to the next as quickly as I can to get the 5 in on a total time as fast as possible. Please clarify.

That's right, take up to 3 minutes rest between rounds and do not count the rest time towards your total.However, if you rest in the midst of a round, say between pull-ups and push-ups, or part way through the squats, it counts.

Look at your day two as more of a strength training day kinda like lifting weights with sets. This is the same thing but you have 3 exercises built into one set. The goal here is to work as hard as you can to complete the exercise without stopping to break until your 3 minute rest. So say you have 5 pullups for each round but can only do 2. Your goal here is to complete 5 pullups without stopping then immediately complete the requisite pushups and squats then rest. These rounds should be a bit harder in that you only stop to rest when you hit your actual rest round of 3 minutes.